Generally speaking, when the temperature of food reaches 30-40 degrees Celsius in summer, it is most likely to deteriorate. But in Japan, this kind of insulated lunch box is called bento, and students often take it to school for lunch. They will choose to cool the food before putting it in the lunch box, so as to ensure that the food will not go bad.
However, if the conditions are good, you can put the food you take to work in the refrigerator and heat it thoroughly in the microwave oven before eating. So you don't have to worry about food going bad.